Development of mechanics of a rocking problem

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The discussion focuses on developing the mechanics of a problem involving an inverted glass cylinder on a table with a mass (coin) on top. The objective is to determine the vertical force and acceleration acting on the coin when the glass is rotated and then released. The glass is considered rigid with negligible mass, and the contact between the glass base and the table is modeled as a linear spring with stiffness K. The relationship between lateral velocity and vertical acceleration of the coin has been established as directly proportional.

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Hector92
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Hi
I want to develop mechanics of a problem which is as follows.

Suppose there is an inverted glass (cylinder) lying on a table. Now suppose there is a mass (or coin) on the top of glass. If we provide an initial rotation to the glass such that only one corner of glass is in contact with table (no overturning) and then release it. Now when the glass will come in full contact with table then the coin will lift vertically. I want to find out the vertical force (acceleration) acting on the top mass or coin using mechanics.

(Suppose glass or cylinder is rigid and with insignificant mass. Only mass acting is the top mass (m). No shear slip. Contact of glass base and table can be represented by a linear spring with stiffness K).

Thanks and Regards
 
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I have found the lateral velocity and vertical acceleration of the top mass and are directly proportional to each other. I want to find out the relationship between two
 

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